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Asst. Prof. Jay Kaiser S. Lariosa
MATH 7
Seminar in Problem Solving
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Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Verbal Problem
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Is a problem of mathematical nature stated in plainwords, and which would involve mathematicalcalculation of some kind before it can be solved.
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Number Related Problems
Chapter 1
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Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Number of Unknowns: 1
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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1.Problems with One UnknownInvolves the determination of the value of a singleunknown as affected by:1.An increase/decrease by whole or fractional amountconcerning its value to form a new number.2.Taking the reciprocal or square value of the unknown.3.In association with whole unit of things or number of people.
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Number of Unknowns: 2
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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2.Problems with Two UnknownsSuggests the nature of greater and smaller numberbeing compared or related.1.Sum or difference of the two2.One is increased or decreased by a certain amount and givento the other3.Sum or difference of the fractional parts of the two4.Sum or product of two consecutive numbers
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Number of Unknowns: 3
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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3.Problems with Three or More Unknowns1.The sum of three numbers of different values2.The sum of three or more consecutive numbers3.Two or three differentiable groups of objects that differ inquantities
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Expressions and its Equivalent
Sample Expressions
i.xplus 5ii.xadded to 7iii.10 increased by kiv.tmore than 8v.5 in addition to gvi.Sum of two numbers pand 9vii.xminus 7viii.Subtract 3 from t
Algebraic Equivalent
i.x+ 5ii.7 + xiii.10 + kiv.8 + tv.g+ 5vi.p+ 9vii.x7viii.t-3
7Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Expressions and its Equivalent
Sample Expressions
i.7 minus xii.cdecreased by 11iii.ndiminished by 8iv.jexceeds by 3 by 5v.wless 10vi.rless than 4vii.dlowered by 6
Algebraic Equivalent
i.7 xii.c11iii.n8iv.j3 = 5v.w10vi.4 rvii.d-6
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Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Expressions and its Equivalent
Sample Expressions
i.The difference between xand 9 is 17ii.2 times a number diii.5% of number wiv.Twice a number qv.Thrice a number avi.The quotient of rand 9vii.The product of 8 and yviii.Half of a number fix.The quotient of x and 4 is 3x.The reciprocal of a number k
Algebraic Equivalent
i.x19 = 17ii.2diii.0.05wiv.2qv.3avi.r/9vii.8yviii.fix.x/4 = 3
x.1/k
9Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Prepared by Asst. Prof. Jay Kaiser S. Lariosa
Expressions and its Equivalent
Sample Expressions
i.Two numbers are consecutive. If one isx, the other is ii.The sum of two consecutive number isiii.The sum of two consecutive odd numberis iv.The square of a number is v.The ratio of xto kis ..
Algebraic Equivalent
i.x+ 1ii.x+ (x+ 1)iii.x+ (x+ 2)iv.x2v.x/k
10Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Linear in One Unknown
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Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Problem Solving Proper
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch12If thrice the number is increased by 11, the result is 35. What is the
number?Step 1: Representation of the unknownLet xbe the number
Step 2: TranslationThrice the number: 3xIncreased by 11: 3x+ 11The result is 35: 3x+ 11 = 35
Step 3: Solve for x.3x= 24x= 24/3x= 8.
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Exercise 1
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch13If twice a number is decreased by 13, the result is 9. What is the number?
Step 1: Representation of the unknownLet xbe the number
Step 2: TranslationTwice the number: 2xDecreased by 13: 2x13The result is 9: 2x13 = 9
Step 3: Solve for x.2x= 22x= 22/2x= 11.
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Exercise 2
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Seven less than twice a number is 15. What is thenumber?
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Exercise 4
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch16The difference between two-thirds of a number and
one-sixth of the same number is seventy-five. Whatis the number?
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Exercise 5
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Two-fifths of a certain number decreased by three-fourths is equal to seven-eights. What is the numbe?
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Exercise 6
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch18If 260 tons of sugar were shipped on Thursday and
this was four times as much as was shipped onWednesday. How many tons were shipped inWednesday?
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Linear in Two Unknowns
19Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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Exercise 7
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
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The sum of two numbers is 39, and their differenceis 7. What are the numbers?
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Exercise 8
Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch
21The sum of two numbers is 24. The greater numberis 10 more than the smaller. What are the numbers?
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